SOLUTION: hi...I was wondering if you could help me with this question as it doesn't seem to make sense to me a bus of 5tons travels at 72km/h and switches off its engine when reaching an

Question 1083576: hi...I was wondering if you could help me with this question as it doesn't seem to make sense to me
a bus of 5tons travels at 72km/h and switches off its engine when reaching an incline of 8 degree's. calculate how far the bus will travel up the incline if friction is not considered
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
Neglecting friction, there is only one force acting on the bus as it moves up the ramp,
and that is the gravitational force directed down the ramp, parallel to the incline.
This force is equal to m*g*sin(theta), where m is the mass of the bus.
The work done on the bus by this gravitational force is equal to the change in
kinetic energy of the bus in coming to a stop, W = delta-K
Since the final kinetic energy is zero, the change in kinetic energy is equal to the initial kinetic energy, K = (m/2)*v^2.
Let d = the distance traveled up the ramp
The work done is W = m*g*sin(theta)*d
W = K: m*g*sin(theta)*d = (m/2)*v^2
Solve for d: d = v^2/(2*g*sin(theta)) [Note that the distance is independent of mass]
Using MKS units, we first convert km/h to m/s: 72 km/h * 1000 m /km * 1 h/3600 s = 20 m/s
Putting in the numbers, we get d = 400/2/9.81/sin(8-deg) = 146.5 m

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